The quantum switch implements indefinite causal order via a coherent control of the orderings of multiple quantum operations, leading to various advantages and applications, one of which being in work extraction where enhancements to daemonic ergotropy is possible. Motivated by recent developments in the connections between non-Markovianity and the quantum switch, we construct a non-Markovian process that reduces to the two-party quantum switch in the fully non-Markovian limit. By controlling the amount of non-Markovianity in the process, we identified two operational regimes with differing behaviors. One has its daemonic ergotropy dependent on the presence and amount of non-Markovianity, achieving the maximum in the quantum switch case of full non-Markovianity. The other regime, however, has no advantages from non-Markovianity. We compare this non-Markovian process with the case of a superposition of independent channels, where two channels are placed in a coherent superposition without indefinite causal order, uncovering the advantages of non-Markovianity. Finally, the conditions required for the production of positive daemonic ergotropy are also derived for the case of fully non-Markovian and fully Markovian limits, where we compare against the conditions required for the superposition of independent channels.
The quantum switch implements indefinite causal order via a coherent control of the orderings of multiple quantum operations, leading to various advantages and applications, one of which being in work extraction where enhancements to daemonic ergotropy is possible. Motivated by recent developments in the connections between non-Markovianity and the quantum switch, we construct a non-Markovian process that reduces to the two-party quantum switch in the fully non-Markovian limit. By controlling the amount of non-Markovianity in the process, we identified two operational regimes with differing behaviors. One has its daemonic ergotropy dependent on the presence and amount of non-Markovianity, achieving the maximum in the quantum switch case of full non-Markovianity. The other regime, however, has no advantages from non-Markovianity. We compare this non-Markovian process with the case of a superposition of independent channels, where two channels are placed in a coherent superposition without indefinite causal order, uncovering the advantages of non-Markovianity. Finally, the conditions required for the production of positive daemonic ergotropy are also derived for the case of fully non-Markovian and fully Markovian limits, where we compare against the conditions required for the superposition of independent channels.
Quantum compositions of channels can grant advantages over classical compositions in quantum information processing or thermodynamical tasks. One of such quantum composition is one with indefinite causal order, where multiple quantum channels are placed in a superposition of different causal or operation orders. The advantages of indefinite causal order were demonstrated in an experimentally realizable setup known as the quantum switch and were often attributed to this new quantum resource of indefinite causality, but some doubts and disagreements still remains as compositions without indefinite causal order can achieve the same advantages. In this work, we proposed that the quantum switch's uniqueness lies in its ability to exhibit coherent non-Markovianity, where memory effects acts across different paths of superposition. We showed that the quantum switch violates completely positive or CP-divisibility and thus has intrinsic non-Markovianity in its evolution, which allows for non-Markovian backflow of information from the environment. This backflow of information can then play a role in the many advantages seen in the quantum switch, and by extending the quantum switch operation such that the non-Markovianity is controllable, we showed that these advantages depend on the presence and amount of non-Markovianity, achieving the quantum switch case when the system is fully non-Markovian. Particularly, we demonstrated this for the quantum switch's advantages in communication capacities, work extraction via daemonic ergotropy, and refrigeration via heat extraction. Other quantum compositions that are often compared to indefinite causal order, such as the superposition of independent channels and superposition of trajectories, are also captured by this extended construction of the quantum switch, and we showed that their difference with the quantum switch lies in the presence or absence of non-Markovianity. Our work suggests that non-Markovianity is an important recipe for the quantum switch or indefinite causal order, and is a nonnegligible factor for its advantages.
Indefinite causal order extends quantum information processing beyond fixed causal structures, with the quantum SWITCH serving as its canonical realization. By coherently superposing different orders of quantum channels, the quantum SWITCH has been shown to provide operational advantages in communication, computation, metrology, and related tasks. Despite these advances, the physical resources responsible for these advantages remains unclear. Recent studies have further revealed that the quantum SWITCH can generate memory effects, manifested as non-Markovian information backflow. In this work, we examine the origin of such memory and determine whether they reflect genuine (quantum) non-Markovianity or instead arises from classical origin. To this end, we analyze two representative scenarios: one based on discrete-time evolution and another formulated through dynamical maps in open quantum systems. We show that the memory effects generated by the quantum SWITCH are not genuinely quantum non-Markovian, thereby prompting a re-examination of the source of quantum advantage in indefinite causal order frameworks.
The quantum switch has seen multiple applications in quantum information and thermodynamical tasks. As it is constructed by placing two quantum channels in a coherent superposition of alternating causal orders, a composition known as indefinite causal order, these enhancements are often attributed to this indefinite causality and coherent superposition. However, as recent works have shown that the quantum switch also features non-Markovian effects that can contribute to the enhancement of communication capacities and work extraction, we attempt to show in this work that these non-Markovian effects can also enhance heat extraction tasks. In particular, we compare the quantum switch to the superposition of independent channels where two quantum channels are placed in a superposition, which have no non-Markovian effects, and show that the quantum switch can only outperform the superposition of independent channels in the prethermalization regimes, which also depends on the presence and amount of non-Markovianity. Our work reveals that positive heat extraction is still possible even when the working body is at a higher temperature than the interacting baths, allowing us to construct a refrigeration cycle utilizing this feature.
The combined use of quantum channels can grant communication advantages in the form of enhancements to communication capacities. One such channel composition is the quantum switch, which implements a system with indefinite causal order by coherent control of the orderings of two or more quantum channels, resulting in enhanced communication capacities. Here, using the monogamy relation, we studied the flow of entanglement monotone in these quantum compositions of channels in the environmental representation. We implemented the two-party quantum switch in this framework, and demonstrated that non-Markovianity is the source of revival of the entanglement monotone in this setup. The possibility and amount of revival was shown to depend on the entangling capability of the channels, and the perfect activation of coherent information with entanglement-breaking channels was also replicated with the perfect revival of entanglement monotone. Additionally, we showed that a more general non-Markovian circuit can still grant enhancements to coherent information and Holevo quantity without the presence of indefinite causal order.
We characterize the impact that the application of two consecutive quantum channels or their quantum superposition (thus, without a definite causal order) has on ergotropy, i.e. the maximum work that can be extracted from a system through a cyclic unitary transformation. First of all, we show that commutative channels always lead to a non-negative gain; non-commutative channels, on the other hand, can entail both an increase and a decrease in ergotropy. We then perform a thorough analysis for qubit channels and provide general conditions for achieving a positive gain on the incoherent part of ergotropy. Finally, we extend our results to d-dimensional quantum systems undergoing a pair of completely depolarizing channels.
Higher-order maps account for the most general transformations in quantum mechanics—they transform input quantum maps to output quantum maps. In this thesis, I focus on the application of such higher-order maps representing two important processes: (1) a particular type of non-Markovian quantum dynamics, and (2) indefinite causal order. First, I will introduce our work on the non-Markovian evolution of quantum states. Such a situation occurs when the past system-environment interaction leads the environment to memorize the information about the system. The measure of the non-Markovianity is given by the temporal correlation among the operations on the system. One way to estimate such correlation is to employ a full tomography of the process matrix, which is computationally intractable. Instead, we utilize machine learning algorithms without using tomographically complete measurement, to estimate the measure of non-Markovianity. We apply our model to a dataset obtained from an optical experiment and show that we are able to predict the measure of non-Markovianity with 90% accuracy. I then introduce various aspects of indefinite causal order. Ordinary experience points only to a definite causal structure, but quantum mechanics admits a more general causal structure that allows for the superposition of different causal orders. That means that the statements, is in the causal past of event B, and B is in the causal past of event A can both be true. The quantum switch can physically realise such an indefinite causal structure where a control quantum system controls the order of operations acting on a target quantum system. Superposition in the control leads to the superposition of the order. We experimentally realise a quantum switch with the control qubit being the polarisation of light and the target qubit being the transverse spatial mode of light. We first verify our quantum switch by measuring a `causal witness'. We then demonstrate an advantage of the quantum switch for classical communication. Finally, I present our work on classical communication through the most general quantum causal structures, represented by the process matrix. We formulate different classical capacities of a bi-partite process matrix. We also study one-way and bidirectional communication protocols through such a process and establish the relevant communication bounds. These enable further analyses of higher-order maps that take advantage of the full suite of processes that quantum mechanics allows.